Hubcount tells you the download count for GitHub releases. Just run it in a git repository that has a GitHub remote:
$ hubcount
GitHub cassava/repoctl
v0.13: (Version 0.13)
repoctl-0.13.tar.gz: 0
v0.12: (Version 0.12)
repoctl-0.12.tar.gz: 0
Compilation and installation requires Go to be available, but then all you need to do is:
$ go get https://github.com/cassava/hubcount